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200 300 400 500 100 200 300 400 500 100 200 300 400 500 100 200 300 400 500 100 200 300 400 500 100 Remainder/ Factor Theorem End Behavior Zeros / Graphs.

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Presentation on theme: "200 300 400 500 100 200 300 400 500 100 200 300 400 500 100 200 300 400 500 100 200 300 400 500 100 Remainder/ Factor Theorem End Behavior Zeros / Graphs."— Presentation transcript:

1 200 300 400 500 100 200 300 400 500 100 200 300 400 500 100 200 300 400 500 100 200 300 400 500 100 Remainder/ Factor Theorem End Behavior Zeros / Graphs PolynomialsExponents

2 Remainder/Factor Theorem 100 Main Get Answer Use the Remainder Theorem to find f(3) for f(x) = 4x 4 – 2x 3 – 10x 2 - 10 A. -10B. -60 C. 125D. 170

3 Use the Remainder Theorem to find f(3) for f(x) = 4x 4 – 2x 3 – 10x 2 - 10 A. -10B. -60 C. 125D. 170 Main Remainder/Factor Theorem 100

4 Main Get Answer Divide 2x 3 + 5x 2 – 7x – 1 by (2x+3) Remainder/Factor Theorem 200

5 Main Remainder/Factor Theorem 200 Divide 2x 3 + 5x 2 – 7x – 1 by (2x+3) x 2 + x – 5 + _14__ (2x+3)

6 Remainder/Factor Theorem 300 Main Get Answer Divide 3x 3 + 16x 2 + 21x + 22 by (x+4)

7 Remainder/Factor Theorem 300 Main 3x 2 + 4x + 5 + _2__ (x+4) Divide 3x 3 + 16x 2 + 21x + 22 by (x+4)

8 Remainder/Factor Theorem 400 If I were to look in the dictionary under the words “greatest” and “math teacher”, whose name would I see? Main Get Answer

9 Remainder/Factor Theorem 400 If I were to look in the dictionary under the words “greatest” and “math teacher”, whose name would I see? KAPLAN ! Come on guys, that was the easiest 400 points in the game! Main

10 Remainder/Factor Theorem 500 Main Get Answer Determine if (x – 2) is a factor of: f(x) = 4x 3 – 9x 2 – 3x + 12

11 Remainder/Factor Theorem 500 Main No, but you must prove it with synthetic division for your points! Determine if (x – 2) is a factor of: f(x) = 4x 3 – 9x 2 – 3x + 12

12 End Behavior 100 Main Get Answer Describe the end behavior of f(x) = -6x 17 + 5x 4 – 8x 2 + 10 As x  +, f(x)  ______ As x  -, f(x)  ______

13 End Behavior 100 Main Describe the end behavior of f(x) = -6x 17 + 5x 4 – 8x 2 + 10 As x  +, f(x)  ______ As x  -, f(x)  ______

14 End Behavior 200 Main Get Answer Describe the end behavior of f(x) = 6x 38 + 5x 3 – 8x + 11 As x  +, f(x)  ______ As x  -, f(x)  ______

15 End Behavior 200 Main Describe the end behavior of f(x) = 6x 38 + 5x 3 – 8x + 11 As x  +, f(x)  ______ As x  -, f(x)  ______

16 End Behavior 300 Main Get Answer Describe the end behavior of f(x) = -x 156 + x 3 – x As x  +, f(x)  ______ As x  -, f(x)  ______ Name one zero. ________

17 End Behavior 300 Main Describe the end behavior of f(x) = -x 156 + x 3 – x As x  +, f(x)  ______ As x  -, f(x)  ______ Name one zero. ________ x = 0

18 End Behavior 400 Main Get Answer Sketch the graph. How many turning points? What are the x-intercepts? f(x) = x 3 – 4x 2 + 4x

19 End Behavior 400 Main Sketch the graph. How many turning points? What are the x-intercepts? f(x) = x 3 – 4x 2 + 4x  (0, 0) and (2, 0) (factor and set factors to 0— What about multiplicity?)  Think about your ends.

20 End Behavior 500 Main Get Answer What is your favorite subject? a) Algebra 2 b) AlgebrA 2 c) Alg. 2 d) Math – specifically Algebra 2

21 End Behavior 500 Main Easy choice! Of course no other subject was even a contender! What is your favorite subject? a) Algebra 2 b) AlgebrA 2 c) Alg. 2 d) Math – specifically Algebra 2

22 Zeros / Graphs 100 Main Get Answer Write a polynomial function of least degree that: has real coefficients, the given zeros of: 1, -1, -7 and a leading coefficient of 1. Put the polynomial in standard form.

23 Zeros / Graphs 100 Main Write a polynomial function of least degree that: has real coefficients, the given zeros of: 1, -1, -7 and a leading coefficient of 1. Put the polynomial in standard form. x 3 + 7x 2 – x – 7

24 Zeros / Graphs 200 Main Get Answer Find all of the possible rational zeros of: f (x) = 3x 5 + 2x 4 – 7x 2 – 9x + 5

25 Zeros / Graphs 200 Main Find all of the possible rational zeros of: f (x) = 3x 5 + 2x 4 – 7x 2 – 9x + 5       

26 Zeros / Graphs 300 Main Get Answer What are all the rational zeros of f(x) = x 3 − 3x 2 − 40x + 84? (You must prove it with synthetic division.)

27 Zeros / Graphs 300 Main What are all the rational zeros of f(x) = x 3 − 3x 2 − 40x + 84? (You must prove it with synthetic division.)            

28 Zeros / Graphs 400 Main Get Answer Use the graph to the right to answer the following: End Behavior: As x  + , f(x)  ______________ As x  - , f(x)  ______________ # Turning Points: _________________________ Degree of polynomial: _________________ You must give me the coordinate (if any) in the following: Absolute Min: _______ Relative Min (Name one.): __________ Absolute Max: _______ Relative Max (Name one.): _________

29 Zeros / Graphs 400 Main Use the graph to the right to answer the following: End Behavior: As x  + , f(x)  ______________ As x  - , f(x)  ______________ # Turning Points: _________________________ Degree of polynomial: _________________ You must give me the coordinate (if any) in the following: Absolute Min: _______ Relative Min (Name one.): __________ Absolute Max: _______ Relative Max (Name one.): _________ -- ++ 4 5 none (-4,-5) or (-1,-2) (-2, 4) or (1,4)

30 Zeros / Graphs 500 Main Get Answer What are all of the zeros of: f(x) = 2x 3 – 11x 2 + 8x – 15

31 Zeros / Graphs 500 Main What are all of the zeros of: f(x) = 2x 3 – 11x 2 + 8x – 15 Graph to find that 5 is a zero. Synthetically divide out the 5.    2x 2 – x + 3 Use quadratic formula:

32 Polynomials 100 Main Get Answer At most, how many roots does the following polynomial have? f(x) = 5x 4 – 2x 3 + x 2 - 7

33 Polynomials 100 Main At most, how many roots does the following polynomial have? f(x) = 5x 4 – 2x 3 + x 2 - 7 

34 Polynomials 200 Main Get Answer Create a polynomial with the following characteristics: quartic, leading coefficient is 9, quadratic coefficient is 4, linear coefficient is –5 and the constant term is –2.

35 Polynomials 200 Main Create a polynomial with the following characteristics: quartic, leading coefficient is 9, quadratic coefficient is 4, linear coefficient is –5 and the constant term is –2. 9x 4 + 4x 2 – 5x – 2

36 Polynomials 300 Main Get Answer If -6/11 is a zero of a polynomial function, what is a factor?

37 Polynomials 300 Main If -6/11 is a zero of a polynomial function, what is a factor? (11x + 6)

38 Polynomials 400 MainGet Answer Find (-5x 2 + 11x – 1) – (6x 2 + 8x – 7)

39 Polynomials 400 Main Find (-5x 2 + 11x – 1) – (6x 2 + 8x – 7) -11x 2 + 3x + 6

40 Polynomials 500 MainGet Answer Factor 8x 3 + 27

41 Polynomials 500 Main Factor 8x 3 + 27 (2x + 3)(4x 2 – 6x + 9)

42 Exponents 100 MainGet Answer (2y -5 )(4x 0 ) Simplify.

43 Exponents 100 Main (2y -5 )(4x 0 ) Simplify.

44 Exponents 200 Main Get Answer (-2x 3 y -3 ) 2 Simplify.

45 Exponents 200 Main (-2x 3 y -3 ) 2 Simplify.

46 Exponents 300 Main Get Answer Simplify.

47 Exponents 300 Main Simplify.

48 Exponents 400 Main Get Answer (4x -2 y) -2 Simplify.

49 Exponents 400 Main (4x -2 y) -2 Simplify.

50 Exponents 500 Main Get Answer Simplify.

51 Exponents 500 Main Simplify.

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